Study of Tunneling Rotation of Methyl Groups by Electron Spin Resonance and Electron Nuclear Double Resonance

Free radicals formed by $\gamma$ irradiation of single crystals of 4‐methyl‐2,6‐di‐tert‐iarybutylphenol are studied by resonance methods at low temperatures. The important part of the radical is the fragment Ċ–CH₃, where the free‐electron spin occupies a $\text{2p}$ orbital centered on the carbon atom attached to the methyl group and experiences a hyperfine interaction with each of the three protons dependent on the proton position, giving rise to structure in the electron spin resonance spectrum which is sensitive to motion of the protons. The hindered methyl group performs torsional oscillations and also undergoes tunneling rotation between its three equivalent orientations, the nuclear spin states being correlated with the motion through the exclusion principle, at least at temperatures sufficiently low for the fragment to be regarded as isolated. An almost symmetrical seven line ESR spectrum is then expected and is observed at 4.2°K. In first order the spectrum is independent of the tunneling frequency when this is large compared with the splitting due to the hyperfine interaction. The tunneling frequency is obtained from small relative shifts of the hyperfine lines measured by electron nuclear double resonance. From the hyperfine interaction tensors, the orientations of the methyl group symmetry axes are found. Above helium temperatures the ESR spectrum undergoes a change which is interpreted in terms of the onset of methyl‐group rotations which are uncorrelated with the proton spin states and occur randomly. From this model, spectra are calculated as a function of the correlation time for the random motion. They show a progressive change from seven lines to the 1:3:3:1 quartet observed at high temperatures. The details of the observed transition are in good agreement.